Vector calibration system

ABSTRACT

Among other things, calibration of a signal processing system is disclosed to minimize vector mismatch between signals frequency-translated from an RF signal and conveyed along a plurality of signal paths of the signal processing system. A calibration signal having a plurality of tones is coupled to the signal processing system such that it is frequency translated. The frequency-translated calibration signal is sampled along a first signal path of the signal processing system to obtain a first set of observed samples. It is also sampled along a second signal path of the system to obtain a second set of observed samples. The first set of observed samples is filtered with an adaptive filter having a set of adaptable coefficients to obtain a set of filtered samples. The coefficients are adapted to minimize undesired deviations between the set of filtered samples and the second set of observed samples.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.09/730,681, filed on Dec. 6, 2000, which claims benefit of U.S.Provisional Application No. 60/190,226, filed Mar. 15, 2000. Both ofthose applications are incorporated herein by reference, and all U.S.patents or patent applications, published or appended articles, and anyother written materials incorporated by reference therein are alsospecifically incorporated herein by reference.

BACKGROUND OF THE INVENTION

Communication systems frequently separate signals by using a pluralityof signal paths that have a predetermined vector relationship. Bysuitably combining the signal paths, such systems can cancel outundesired signals by mathematically exploiting predetermined phase andamplitude relationships between respective signal vectors of each signalpath.

Quadrature image rejection receivers employ signal paths having aquadrature relationship to discriminate between signals having positivefrequency (above DC) and negative frequency (below DC). Quadraturedirect conversion receivers separate points in a two-dimensional signalspace using the orthogonality of quadrature signals to define axes ofthe signal space. Array processors couple signal processing circuitry toarray elements (e.g., antennas, ultrasonic transducer elements, etc.)via signal paths having particular phase and amplitude relationships todefine a desired beam pattern. For example, an array beamformer mayprovide signal paths to antenna elements of an array with equal phaseand a windowed (i.e., tapered) distribution of amplitudes to define abroadside beam having superior sidelobe rejection. The beamformer mayvary the gain and/or phase between elements to steer the beam to aparticular deviation from broadside.

Many communication systems require precise vector matching betweensignal paths to achieve a high degree of separation between desired andundesired signals. To obtain 50 dB of quadrature image rejection, forexample, an in-phase and quadrature signal are required to have no morethan about 0.6% amplitude mismatch and about ±0.4 degrees of phasemismatch from quadrature. Comparable levels of vector matching arerequired between elements of an array having 50 dB of sideloberejection.

Conventional communication systems employ digital signal processing todetermine vector mismatch between signal paths and correct the mismatch.The precision to which such systems can correct mismatch is limited,however, because the mismatch often varies with frequency and isdifficult to determine with enough precision to achieve high separationbetween desired and undesired signals. Consequently, the need remainsfor determination of vector mismatch across a range of frequencies andwith greater accuracy.

SUMMARY OF THE INVENTION

According to various aspects and methods of the present invention, asignal processing system determines vector mismatch between a pluralityof signal paths. Advantageously, such a system can determine mismatchacross a range of frequencies. A signal generator can provide a periodiccalibration signal having a plurality of frequency components. Thesystem frequency translates the calibration signal to provide a firstset of observed samples. The first sample set is compared to a secondset of samples, which are modeled by a function of parameters includingan estimated vector mismatch and a plurality of basis functions. A valueof vector mismatch is determined (at least to an estimate) thatminimizes the difference between the first sample set and the secondsample set.

According to one advantageous aspect of the invention, the calibrationsignal comprises multiple tones having predetermined gain, phase andfrequency relationships to each other. By providing a periodiccalibration signal with a plurality of tones, the signal processingsystem is able to concurrently determine vector mismatch at thefrequency of each tone. Consequently, the system can determine mismatchacross a range of frequencies simply and efficiently.

By minimizing the difference between a set of observed samples and a setof samples modeled by basis functions, the system can determine vectormismatch using linear techniques. According to various advantageousaspects of the invention, deterministic least squares can be employed.Straightforward and efficient recursive techniques such as least meansquares (LMS) and recursive (i.e., adaptive) least squares (RLS) canalso be employed.

By continuously or periodically updating its determination of vectormismatch, a system according to a further aspect of the invention canaccommodate nonstationary (i.e., time-varying) errors.

A system according to another advantageous aspect of the presentinvention provides a phase-synchronous calibration signal. Afterfrequency translation, components of a phase-synchronous calibrationsignal are matched in frequency with components of modeled signals,which are mathematically modeled by one or more basis functions. In onesuch system, a baseband calibration signal that is phase-synchronouswith the basis functions is frequency translated to RF with a firstmixer and frequency translated again to baseband or a low-IF frequencyrange with a second mixer or pair of mixers. Advantageously, the firstmixer and second mixer (or mixer pair) can be fed by signals from thesame local oscillator output. Thus, the frequency-translated calibrationsignal remains phase-synchronous with the basis functions even when thelocal oscillator output is subject to phase variations.

A system according to still another advantageous aspect of the presentinvention provides a plurality of first sample sets. The systemdetermines, at least to an estimate, a plurality of vector mismatchvalues by comparing each respective first sample set to a respectivesecond sample set modeled by basis functions and minimizing thedifference between the compared sample sets. By statistically combiningthe values of vector mismatch determined for each one of the pluralityof first sample sets, such a system can improve accuracy of the mismatchdetermination while keeping the interval of each sample set relativelyshort. Sample sets having shorter intervals are less prone to problemscaused by local-oscillator induced phase variation between thefrequency-translated calibration signal and the basis functions.

Quadrature receiver and array processor systems operating in accordancewith further aspects of the invention determine and correct vectormismatch across a range of frequencies, thus providing improvedperformance. Vector mismatch between in-phase and quadrature signalpaths can be more accurately and efficiently determined and correctedacross a range of frequencies to improve demodulator performance orimage rejection. Similarly, vector mismatch between array elements canbe better determined and corrected to improve array efficiency andsidelobe rejection.

BRIEF DESCRIPTION OF THE DRAWING

Various embodiments of the present invention are described below withreference to the drawing, wherein like designations denote likeelements.

FIG. 1 is a schematic block diagram of a radio receiver implementingfunctions of a vector calibration system according to various aspects ofthe present invention.

FIG. 2 is a schematic block diagram of a digital signal processor of thereceiver of FIG. 1.

FIG. 3 is a schematic block diagram of a baseband calibration signalgenerator of the receiver of FIG. 1.

FIG. 4 is a functional block diagram illustrating functions performedaccording to various aspects of the present invention by the digitalsignal processor of FIG. 2.

FIG. 5 is a flow diagram of a method of the invention for vectormismatch determination using deterministic least-squares processing.

FIG. 6 is a flow diagram of a method of the invention for vectormismatch determination using Least Mean Square (LMS) processing.

FIG. 7 is a flow diagram of a method of the invention for vectormismatch determination using Recursive Least Square (RLS) processingwith an exponential forgetting window.

FIGS. 8-10 are simulated time-domain plots illustratingfrequency-translated quadrature calibration signals suitable for use inthe receiver of FIG. 1, wherein the signals are mismatched in phase froma quadrature relationship.

FIGS. 11-13 are simulated time-domain plots illustratingfrequency-translated quadrature calibration signals suitable for use inthe receiver of FIG. 1, wherein the signals are mismatched in amplitudefrom a quadrature relationship.

FIGS. 14-16 are simulated time-domain plots illustratingfrequency-translated quadrature calibration signals suitable for use inthe receiver of FIG. 1, wherein the signals are mismatched in both phaseand amplitude from a quadrature relationship.

FIGS. 17 and 18 are simulated plots of a residual signal envelope andsmoothed envelope, respectively, illustrating reduction of thedifference between an observed calibration signal and a modeledcalibration signal during simulated operation of vector mismatchcalibration according to various aspects of the present invention.

FIGS. 19-21 are simulated plots of relative amplitude (in dB) of anundesired image signal, illustrating improvement in image rejectionduring simulated operation of vector mismatch calibration according tovarious aspects of the present invention.

FIG. 22 is a simulated frequency-domain plot illustrating frequencyresponse of an exemplary noise reduction filter that may be used duringvector mismatch calibration according to various aspects of the presentinvention.

FIG. 23 is a simulated frequency-domain plot illustrating frequencyresponse of the filter of FIG. 22 when implemented at a 360 kHz samplerate.

FIG. 24 is a simulated frequency domain plot illustrating frequencyresponse of an exemplary anti-aliasing filter of the receiver of FIG. 1and the filter of FIG. 22 when implemented at a 360 kHz sample rate.

FIG. 25 is a simulated frequency-domain plot illustrating a cascadedfrequency response of the filters of FIG. 15.

FIG. 26 is a schematic block diagram of an array processor implementingfunctions of a vector calibration system according to various aspects ofthe present invention.

DESCRIPTION OF PREFERRED EXEMPLARY EMBODIMENTS

A vector calibration system according to various aspects of the presentinvention provides numerous benefits, including concurrently determiningvector mismatch between a plurality of signal paths across a range offrequencies. Such a system can be advantageously implemented in anycommunication system that separates signals using a plurality of signalpaths having a predetermined vector relationship. As may be betterunderstood with reference to FIG. 1, for example, a low-IF receiver 100employs quadrature signal paths to separate desired signals from imagesignals having opposite frequencies. Conventional low-IF (lowintermediate frequency) receivers reduce the complexity of IF processingby performing the processing at frequencies that are much closer to thebaseband frequency range of a signal of interest than the RF frequencyof the signal. In a receiver variation having circuitry similar to thatof receiver 100, quadrature signal paths are employed to separatefrequency components of a signal that is directly converted to basebandfrequencies. In accordance with the invention, receiver 100 includeshardware and software for correcting mismatch from a quadraturerelationship across its low-IF frequency range.

As discussed in detail below, receiver 100 includes, inter alia, acalibration signal subsystem 150 for implementing an exemplary vectorcalibration system. Receiver 100 also includes circuitry thatconventionally converts a selected radio frequency (RF) signal tobaseband information. This circuitry includes an RF input port 102(e.g., a suitable type of coaxial connector), a front-end stage 104, afrequency translation subsystem 110, a digital subsystem 130, a controlsubsystem 140, and a clock generator 145.

Front-end stage 104 receives RF signals from input port 102 andamplifies the signals using a conventional low-noise amplifier.Preferably, front-end stage 104 selectively amplifies signals from afrequency band of interest (e.g., one of the frequency bands forcellular telephone downlink signals) while at least partially rejectingsignals outside the band of interest. Front-end stage 104 couples theamplified signals to frequency translation subsystem 110 through aswitching device 106, the purpose of which is discussed below. Frequencytranslation subsystem 110 conveys the selected RF signal to digitalsubsystem 130 in a frequency translated, filtered form. Digitalsubsystem 130 samples and digitizes the selected frequency-translatedsignal and subjects the signal to further signal processing in thedigital domain. Clock generator 145 provides synchronized clock signalsto various portions of receiver 100, preferably by dividing down thehigh frequency output of a high-stability master oscillator (e.g., atemperature-compensated crystal oscillator) by various divide ratios.(Even-numbered divide ratios are preferred, with powers of two beingparticularly efficient to implement.)

Frequency translation subsystem 110 includes a pair of mixers 112 and114, a local oscillator 116, and bandpass filters 118 and 119. Localoscillator 116 provides in-phase and quadrature outputs to mixers 112and 114, respectively. Responsive to the RF input from front-end stage104 and respective inputs from local oscillator 116, mixers 112 and 114translate RF signals of interest into in-phase and quadrature signals,respectively, within a low-IF frequency range. The in-phase andquadrature signals are filtered by respective bandpass filters 118 and119 to perform an initial selection of a relatively narrow frequencyrange of interest (e.g., one signal channel) within the low-IF frequencyrange.

Digital subsystem 130 includes A/D converters 120 and 122 and a digitalsignal processor (DSP) 132. A/D converters 120 and 122 sample thein-phase and quadrature signals, respectively, from frequencytranslation subsystem 110 and convert the signals into digital data.Bandpass filters 118 and 119 of frequency translation subsystem 110 arepreferably configured to substantially reject signals at frequenciesabove the low-IF frequency range that would alias into the frequencyrange after sampling. (As set forth in Appendix D, lowpass filters canalso be employed.) A/D converters 120 and 122 convey the digital data toDSP 132 in any suitable format, serial or parallel. DSP 132 performsdigital signal processing. Preferably, this processing includes (1)selecting a signal of interest from within the low-IF frequency range ofthe signals represented by the digital data, (2) rejecting signalswithin an undesired image frequency range opposite the frequency ofinterest, and (3) translating the signal of interest into a basebandoutput signal. The baseband output signal can be a spectral copy of thesignal of interest that has been frequency translated to basebandfrequencies. Alternatively, the baseband output signal can be arepresentation of baseband information demodulated from the signal ofinterest.

Functions of frequency translation subsystem 110 and digital subsystem130 can be implemented by any suitable hardware and/or software. Forexample, U.S. Pat. No. 5,937,341 issued Aug. 10, 1999 to Suominendiscloses suitable hardware and software that provides particularadvantages including simplified tuning of local oscillator 116 andreduced computational burden in DSP 132. This aforementioned patent isreferred to herein as the '341 patent. The detailed description portionof the '341 patent (and referenced drawing figures) is incorporatedherein by reference. The detailed description portions of any patents orpatent applications referenced in the '341 patent are also specificallyincorporated herein by reference.

As discussed above, receiver 100 employs in-phase and quadrature signalpaths to separate signals of interest from image signals havingfrequencies of equal magnitude but opposite sign (i.e., inverse ormirror frequencies). Circuitry in the in-phase signal path includesmixer 112, bandpass filter 118, and A/D converter 120. Circuitry in thequadrature signal path includes mixer 114, bandpass filter 119, and A/Dconverter 122. The separation between signals of interest and imagesignals in receiver 100 is degraded by vector mismatch between thein-phase and quadrature signal paths. (In a variation, a single A/Dconverter samples both the in-phase and quadrature signals.)

Vector mismatch between the in-phase and quadrature signal paths canarise from a number of sources including deviations from a quadraturerelationship between 0 degree and 90 degree output signals of localoscillator 116, variations in mixers 112 and 114, variations in thetransfer functions of filters 118 and 119, varying sensitivity of A/Dconverters 120 and 122, and variations in propagation delay betweenthese components. Frequently, the vector mismatch caused by thesesources various as a function of frequency. For example, varyingtransfer functions of bandpass filters 118 and 119 can causefrequency-dependent vector mismatch across the low-IF frequency range ofreceiver 100.

Receiver 100 implements functions of a vector calibration system tocorrect vector mismatch and thus improves separation between signals ofinterest and image signals. A vector calibration system according tovarious aspects of the present invention can be implemented by anysuitable combination of analog circuitry, digital circuitry, and/orsoftware that controls execution of software-based digital circuitry toperform computations and digital signal processing functions. Forexample, circuitry of receiver 100 includes circuitry that is configuredfor implementing an exemplary vector calibration system, including clockgenerator 145, a calibration signal subsystem 150, switching device 106,and digital subsystem 130. Calibration signal subsystem 150 generates anRF calibration signal S2 having frequency components within thefrequency band of interest. Clock generator 145 provides a time base forthe calibration signal. Frequency translation subsystem 110 translatesthe RF calibration signal back down in frequency, (to the low-IF rangeof frequencies employed by receiver 100) to provide an in-phasecalibration signal S3 a and a quadrature calibration signal S3 b.

Digital subsystem 130 digitizes calibration signals S3 a and S3 b toprovide a set of observed samples and implements functions of a vectorcalibration system that determines vector mismatch based on thosesamples. The vector calibration system also performs suitable digitalsignal processing to at least partially correct the vector mismatch. Anexemplary multi-frequency vector calibration system 400 that can beimplemented by hardware and/or software of digital subsystem 130 may bebetter understood with reference to the functional block diagram of FIG.4. Digital subsystem 130 also implements functions of a conventionalbaseband translator 440, for example in accordance with the disclosureof the '341 patent. In a variation employing direct-conversion (e.g.,frequency translation directly from RF to baseband) baseband translator440 can be a conventional quadrature direct-conversion tuner(implemented digitally).

Functional blocks of exemplary system 400 include a sample modeling andmismatch determination subsystem 410, a correction coefficient generator420, and a digital filter 430. In receiver 100, system 400 receivescalibration signals S3 a and S3 b from frequency translation subsystem110 via in-phase and quadrature inputs, labeled in FIG. 4 as I and Q.Based on the calibration signals S3 a and S3 b, sample modeling andmismatch determination subsystem 410 determines a mismatch parametervector β that is representative of vector mismatch between the in-phaseand quadrature signal paths. Correction coefficient generator 420converts the mismatch parameter vector β into correction coefficientsthat digital filter 430 employs to correct the vector mismatch.

Sample modeling and mismatch determination subsystem 410 compares theobserved samples from digitized calibration signals S3 a and S3 b to aset of modeled samples, which it generates either as actual samples orconceptually. Subsystem 410 models the modeled samples as a function ofparameters including an estimated vector mismatch and a plurality ofbasis functions. Subsystem 410 determines a value of vector mismatchthat minimizes the difference between the observed samples and themodeled samples.

The modeling function can include other parameters, for examples indiciaof environmental conditions. A communication system implementing vectormismatch calibration according to the invention can include one or moreenvironmental sensors for providing indicia of one or more environmentalconditions. One example of an environmental conditions that caninfluence vector mismatch is temperature of circuitry in thecommunication system. Another environmental condition that can bedetermined by circuitry controlling the local oscillator of acommunication system is the frequency of local oscillator. The localoscillator may have quadrature signals whose phase relationship variessomewhat over a frequency range. Incorporating the local oscillatorfrequency to the model may help improve its accuracy.

Vector β can consist of the amplitudes of each basis function used tomodel samples matching the observed samples of signals S3 a and S3 b.This exemplary form of parameter vector β is discussed in detail belowwith reference to FIGS. 5-7 and Appendices A,B, and C, which areintegral to the specification of this application and incorporated byreference as discussed below.

Correction coefficient generator 420 and digital filter 430 cancooperate in any suitable manner to correct vector mismatch based on amismatch parameter vector β. When vector β represents amplitudes ofmodeling basis functions, for example, correction coefficient generator420 can compute amplitude and phase mismatch between signal paths basedon the basis function amplitudes. Appendix A describes an example ofsuch a computation, particularly with reference to equations labeled(11) and (12).

Advantageously, calibration signals S3 a and S3 b have multiple tones inexemplary receiver 100 and system 400. (Appendix B discloses a two-tonecalibration signal.) Using the values of amplitude and phase mismatchthat it computes at each tone of calibration signals S3 a and S3 b,generator 420 can form complex exponentials corresponding tofrequency-dependent vector mismatch. Generator 420 can then derivecoefficients of an impulse response that is inversely representative ofthe vector mismatch based on the complex exponentials. Generator 420 canderive these coefficients by applying the complex exponentials toappropriate frequency bands of an inverse fast Fourier transform (IFFT).Digital filter 430 realizes this impulse response, preferably as anfinite-impulse-response (FIR) filter.

In a variation of subsystem 400, a conventional adaptive FIR is employedto correct vector mismatch without the need for the vector mismatch tobe determined. Since the desired relationship of calibration signals S3a and S3 b to baseband calibration signal S1 is known (or easilydetermined), an error signal (i.e., the difference between observed andmodeled samples) can be generated that reflects the deviation(s) of S3 aand S3 b from the ideal. This error signal can then be incorporated intoa conventional LMS algorithm for determining the adaptive FIR filtercoefficients. In this advantageous variation, the estimated parametervector directly contains the FIR filter coefficients. In this variation,the difference between the first sample set (observed samples) and thesecond sample set (actual or conceptual modeled samples) is minimizednot to determine a value of vector mismatch, but to correct the mismatchwithout needing to know what it is.

Operation of exemplary receiver 100 and vector calibration system 400may be better understood with reference to simulation plots of FIGS.8-15. In the simulation, receiver 100 is a low-IF receiver configured toselect one of three frequency-translated channels from a low-IFfrequency range between 60 kHz and 120 kHz. The three channels have 20kHz bandwidth and are adjacent. If desired, receiver 100 can beconfigured in accordance with the disclosure of the '341 patent toobtain improved digital signal processing efficiency and doubled localoscillator step size (e.g., 120 kHz instead of 60 kHz). Calibrationsignal subsystem 150 provides RF calibration signal S2 with componentsat three offset frequencies above and below the output frequency oflocal oscillator 116. These offset frequencies are ±70 kHz, ±90 kHz, and±110 kHz. Frequency translation subsystem 110 converts signal S2 intoin-phase and quadrature signals S3 a and S3 b using the same outputfrequency of local oscillator 116. Thus, signals S3 a and S3 b eachcontain three tones (at 70, 90, and 110 kHz), which are matched to theoffset frequencies of signal S2. (The simulation assumes that frequencytranslation of signals S1, S2, and S3 a, S3 b causes no gain or phasedistortion of the calibration signals.)

Vector mismatch between signal paths of frequency translation subsystem110 cause calibration signal S3 a and S3 b to differ. FIGS. 8, 11, and14 are time-domain plots illustrating calibration signals S3 a and S3 bon the same axes with differences caused by phase-only, amplitude-only,and phase/amplitude types of vector mismatch. FIGS. 8-10 illustratedifferences caused by phase mismatch between signal paths, FIGS. 11-13illustrate differences caused by amplitude mismatch, and FIGS. 14-16illustrate differences caused by vector mismatch comprising both phaseand amplitude mismatch. In FIGS. 8-10, the 70, 90, and 110 kHz tones ofsignals S3 a and S3 b have relative amplitudes (i.e., amplitude-typevector mismatch) of −1, 0, and +1 dB, respectively. In FIGS. 11-13,these tones have relative phases (i.e., phase-type vector mismatch) of+1, 0, −2 degrees, respectively. In FIGS. 14-16, these tones have thecombined vector mismatches illustrated in FIGS. 8-10 and FIGS. 11-13(phase/amplitude-type vector mismatch).

Each plot of FIGS. 8-10 includes a respective dashed box 910, 1110, and1410 highlighting a sub-interval within the interval of the plots. Inthis time interval, differences between signals S3 a and S3 b areparticularly apparent. FIGS. 9, 12, and 15 are time-domain plotsillustrating calibration signals S3 a and S3 b within the sub-intervalof dashed boxes 910, 1110, and 1410. FIGS. 10, 13, and 16 aretime-domain plots illustrating signals of the difference between thecalibration signals S3 a and S3 b (i.e., a residual signal) illustratedin FIGS. 8, 11, and 14, respectively.

A vector mismatch calibration system according to various aspects of thepresent invention determines (at least to an estimate) a value of vectormismatch that minimizes (at least down to an acceptable local minimum orthe system noise level) the difference between samples of an observedcalibration signal and samples of a modeled calibration signal. Thesystem compares the observed samples are compared to the modeled sampleswithout the modeled samples necessarily needing to be stored in anyseparate form. In other words, the modeled samples may exist onlymathematically in the equations used during comparison. The systemgenerates the modeled (again, not necessarily as actual data values) bya mathematical function of parameters including (1) an estimated vectormismatch (e.g., estimated phase and/or amplitude) and (2) a plurality ofbasis functions. This modeling is discussed in further detail below withreference to FIGS. 4-7. The parameters can also include indicia ofenvironmental conditions such as temperature or local oscillatorfrequency.

An actual vector calibration system of the invention using discrete-timeprocessing compares samples of observed and modeled signals rather thanactual continuous-time signals. However, the comparison process maybetter understood (with reference to the plots of FIGS. 8-10) by viewingsignal S3 b as the observed signal and signal S3 a as the modeledcalibration signal. The more the system can minimize the differencebetween signals S3 a and S3 b, the smaller the residual signal of FIGS.10, 13, and 16 will become. To minimize this difference and thus modelthe observed calibration signal, the system seeks to minimize theamplitude of the residual signal, either iteratively ordeterministically.

Initially, the residual signal can be expected to have a relatively highamplitude because the absolute phase of the observed calibration signalis not known. In receiver 100, the observed calibration signals S3 a andS3 b are filtered component signals of a frequency-translatedcalibration signal S3, which is derived from RF calibration signal S2,which is a frequency-translated copy of baseband calibration signal S1.In other words, the signal flow is as follows: S1 (baseband) to S2 (RF)to S3 (frequency-translated) to S3 a and S3 b (filtered, quadraturesplit). Even though the modeled calibration signal can be matchedrelatively closely in phase to the originating baseband calibrationsignal S3, the intervening signal processing that converts signal S3 toobserved calibration signal S3 a or S3 b causes unpredictable phaseoffsets. Fortunately, the absolute phase is unimportant. The inventivevector mismatch calibration system only needs to determine the relativephases between two or more signal paths, not their absolute phase delay.

FIGS. 17 and 18 are simulated plots of a residual signal envelope andsmoothed envelope, respectively, illustrating reduction of the residualsignal during operation of the vector calibration system. As theresidual signal amplitude diminishes, the modeled calibration signalmore closely approximates the observed calibration signal and the vectorcalibration system converges to a more accurate determination of vectormismatch.

FIGS. 19-21 are simulated plots of the relative amplitude of anundesired image signal (in dB), illustrating increasing image rejectionduring operation of the vector calibration system. FIG. 19 illustrateundesired image signal amplitude at the center of the 70 kHz channel ofexemplary receiver 100, while FIGS. 20 and 21 illustrate undesired imagesignal amplitude for the 90 and 110 kHz channels, respectively. As thesystem converges to a more accurate determination of vector mismatch,the mismatch can be corrected more accurately. Image rejection improvesas a result.

FIGS. 22-25 are simulated frequency-domain plots illustrating frequencyresponse of analog and digital filters of exemplary receiver 100.Receiver 100 implements analog (i.e., continuous-time) filtering inbandpass filters 118 and 119, and implements digital (i.e.,discrete-time) filtering as part of sample modeling and mismatchdetermination subsystem 410. Subsystem 410 performs digital filtering ofthe in-phase and quadrature signals entering digital subsystem 130before it performs sample modeling and mismatch determination. Becauseexemplary calibration signals S3 a and S3 b of receiver 100 containtones only at desired frequencies, filtering can be omitted forsimplicity but at the expense of increased overall noise levels. Invariations where the calibration signal(s) contain undesired tones,filtering is more important to ensure convergence of sample modeling.

FIG. 22 illustrates the baseband frequency response of an exemplarydigital filter implemented in subsystem 410, across a frequency rangetwice the Nyquist limit of the filter. FIG. 23 illustrates frequencyresponse of the filter of FIG. 22 when digital subsystem 130 processessignals entering the digital filter at a 360 kHz sample rate. Thisfrequency response has deep but narrow spectral nulls, which provideparticular advantages for certain types of calibration signals, asdiscussed in further detail below.

FIG. 24 is a simulated frequency domain plot illustrating an exemplaryfrequency response of bandpass filters 118 and 119 in dashed lines andthe digital filter of subsystem 410 (when implemented at a 360 kHzsample rate) in solid lines. The frequency response of bandpass filters118 and 119 reaches a significant level of stop band attenuation by thetime the frequency of response of the digital filter reaches its firstalias, at about 240 kHz.

FIG. 25 is a simulated frequency-domain plot illustrating a cascadedfrequency response of bandpass filters 118 and 119 and digital filter ofsubsystem 410. The respective filters add several dB of ripple to thepassband of receiver 100.

A multi-tone calibration signal according to various aspects of thepresent invention can be employed to correct passband ripple without theneed for adaptive equalization of a received signal. The inventivecalibration signal can be applied even in communication systems wherethe benefits of vector mismatch calibration are not required. Forexample, a conventional superheterodyne receiver can benefit from ripplecorrection using a phase-coherent calibration signal even though such areceiver may not have multiple signal paths that could benefit fromvector mismatch calibration. A calibration signal subsystem according tovarious aspects of the present invention (e.g., subsystem 150) can beadvantageously employed in such a receiver to quickly and efficientlycorrect ripple across a range of frequencies. A sample modeling andmismatch determination subsystem according to various aspects of theinvention can be suitably adapted for calibrating mismatch between aknown baseband calibration signal (e.g., S1 of receiver 100) and anobserved calibration signal (e.g., S3 a, S3 b). Such calibration canalso be performed in conjunction with vector mismatch calibration.Passband ripple can also be conventionally equalized.

A calibration signal subsystem according to various aspects of theinvention includes any suitable hardware and/or software for generatingan RF calibration signal having a frequency component at the frequencyof a potential RF signal of interest. Such hardware and/or software canbe integrated into the circuitry and/or software of a vector calibrationsystem according to the invention, or into a device incorporating suchcircuitry. Alternatively, separate hardware and/or software canimplement functions of a calibration signal subsystem during a one-timecalibration process. For example, manufacturing or maintenance testequipment can implement a calibration signal subsystem to perform aone-time calibration of a communication receiver that contains circuitryand software of the inventive vector calibration system. Such a receivercan include a nonvolatile memory device (e.g., flash memory) to retaindata resulting from the calibration.

According to a particularly advantageous aspect of the invention, thecalibration signal can include multiple RF frequency components (i.e.,tones) that the receiver can frequency translate to a single IFfrequency range. When the calibration signal comprises multiple toneshaving predetermined phase and frequency relationships to each other, avector calibration system of the invention can determine vector mismatchat the frequency of each tone concurrently. As a result, the system candetermine mismatch across a range of frequencies simply and efficiently.

As may be better understood with reference to FIGS. 1-3, exemplarycalibration signal subsystem 150 includes a calibration signal generator152, a mixer 154, and a local oscillator phase adjustor 156. Controlledby clock generator 145, calibration signal generator 150 provides abaseband calibration signal S1 having multiple tones, as is preferred,within the low-IF frequency range of receiver 100. Mixer 154 translatescalibration signal S1 to an RF calibration signal S2 in the RF frequencyrange of several potential signals of interest, e.g., adjacent channelsof a channelized frequency spectrum. Mixer 154 uses the same outputsignal of local oscillator 116 that mixer 112 would use when frequencytranslating one of the potential signals of interest.

According to a particularly advantageous aspect of the presentinvention, a single local oscillator can provide a shared phase-coherentsignal for both translation of the calibration signal from baseband toRF (S1 to S2) and translation of the RF calibration signal back tobaseband (S2 to S3 a, S3 b). For example, the in-phase (0-degree) outputof local oscillator 116 feeds both mixer 154 and mixer 112.Phase-synchronous local oscillator signals perform frequency translationof (1) the baseband components from calibration signal generator 152 toRF and (2) the RF-translated calibration signal to its original basebandfrequency, within its low-IF frequency range. When it reaches digitalsubsystem 130, quadrature calibration signals S3 a and S3 b arephase-synchronous (i.e., having matched frequencies) with basisfunctions that vector calibration subsystem 400 (FIG. 4) models againstthe calibration signal to determine vector mismatch. Thefrequency-translated calibration signals remain phase-synchronous withthe basis functions even when the local oscillator output is subject tophase variations.

A calibration signal generator of a calibration signal subsystem (e.g.,subsystem 150) can provide a baseband calibration signal by any suitabletechnique, using analog and/or digital signal processing. As may bebetter understood with reference to FIG. 3, for example, calibrationsignal generator 152 generates a three-tone calibration signal S1primarily using digital signal processing. (The tones of this exemplarysignal are not necessarily phase-optimized for minimum peak amplitude,but lack of such optimization is not important for a signal having onlythree tones.) Generator 152 includes a state machine 310 for generatingdigital output values and a D/A converter 320. State machine 310 changesstates at a 180 kHz rate, as controlled by a clock signal (e.g., 360kHz) from clock generator 145. Each time state machine 310 changesstates, it provides a new digital output that D/A converter 320 convertsinto an analog sample of the baseband calibration signal S1. Lowpassfiltering can follow D/A converter 320 to limit the bandwidth of the RFcalibration signal provided by mixer 154.

TABLE I below illustrates exemplary output values of signal generator152 for a baseband calibration signal having three primary tones. Whenprovided periodically at a sample rate of 180 kHz, these 18 outputvalues form a periodic calibration signal with tones at 70 kHz, 90 kHz,and 110 kHz. The 110 kHz frequency component is the first alias of the70 kHz component. State machine 310 can generate these values using fivepreset multipliers labeled A,B,C,D, and zero with varying sign. Thus,state machine 310 needs only to store four separate digital values.State machine 310 can provide any desired one of the 18 repeated outputvalues of TABLE I by selecting the desired digital value and multiplyingit by the desired ±sign.

In a variation of baseband calibration signal generator 152, the presetmultipliers are integrated into D/ A converter 320. In such a variation,D/A converter 320 is only capable of providing nine distinct outputvalues. (These are the four preset multipliers with both possible signsplus zero.) Such a variation is particularly inexpensive to implement onan integrated circuit that already includes precision analog circuitry,for example circuitry implementing functions of frequency translationsubsystem 110. TABLE I Sample Output Preset Multiplier 00.16666666666667 +A 1 −0.14067160479100 −B 2 0.07484979751855 +C 30.00000000000000 Zero 4 −0.04885473564288 −D 5 0.04885473564288 +D 60.00000000000000 Zero 7 −0.07484979751855 −C 8 0.14067160479100 +B 9−0.16666666666667 −A 10 0.14067160479100 +B 11 −0.07484979751855 −C 120.00000000000000 Zero 13 0.04885473564288 +D 14 −0.04885473564288 −D 150.00000000000000 Zero 16 0.07484979751855 +C 17 −0.14067160479100 −B

In an advantageous variation of calibration signal subsystem 150,baseband calibration signal generator 152 generates a harmonic richbaseband calibration signal S1 (e.g., a square wave) at a desiredfundamental frequency (e.g., 10 kHz). The fundamental frequency isselected to produce harmonics at desired calibration tone frequencies.For example, a 10 kHz fundamental square wave modulating mixer 154 willproduce harmonics at the offset frequencies of ±70 kHz, ±90 kHz, and±110 kHz that are desired in receiver 100. The undesired harmonics(e.g., 30, 50, 130 kHz) can be filtered out in digital filtering ofsample modeling and mismatch determination subsystem 410. Such filteringmay be better understood with reference to exemplary frequency responseplots of FIGS. 22-25. This frequency response has deep but narrowspectral nulls at the frequency of the undesired harmonics.

Calibration signal subsystem 150 includes a local oscillator phaseadjustor 156, which adjusts the phase of the signal from localoscillator 116 by an amount controlled by control subsystem 140.(Control subsystem 140 can be implemented by software of DSP 132 or in aseparate microcontroller IC, clocked by clock generator 145 asillustrated in FIG. 1.) A local oscillator phase adjustor according tovarious aspects of the present invention can include any structure forvarying the propagation delay or phase of a local oscillator signal. Anexample of a suitable phase adjustor is an electronically variablecapacitance device (i.e., a varactor) controlled by an analog voltagefrom control subsystem 140. The higher the capacitance of such a device,the more it delays local oscillator phase.

Phase adjustor 156 can be controlled to maximize the accuracy of vectormismatch calibration according to any suitable technique. Accuracy canbe expected to be optimal when the phase of the local oscillator signalat the input of mixer 154 is midway the phase of that signal at theinput of mixers 112 and 114. In other words, the local oscillator signalat the input of mixer 154 is preferably (1) offset +45 from the localoscillator signal at the input of mixer 112 and (2) offset −45 degreesfrom the local oscillator signal at the input of mixer 114.

When local oscillator phase adjustor 156 has a known control vs. phaseshift transfer function (preferably linear over the range of interest),an optimal phase offset can be determined by setting the phase offset toa point midway between two phase offsets that null out calibrationsignals S3 a and S3 b, respectively. An exemplary technique forcontrolling phase adjustor 156 includes steps of (1) adjusting phaseadjustor 156 to a first phase setting to minimize amplitude ofcalibration signal S3 a, (2) adjusting phase adjustor 156 to a secondphase setting to minimize amplitude of calibration signal S3 b, (3) andsetting phase adjustor 156 to a third phase setting that is midwaybetween the first phase setting and the second phase setting. Forexample, if the first phase setting is 10 degrees and the second phasesetting is 100 degrees, the third phase setting is determined as 55degrees.

Appendix B provides disclosure of a method for dealing with an undesiredphase offset, which may be instructive in operation of a localoscillator phase adjustor according to various aspects of the presentinvention.

As may be better understood with reference to FIG. 2, digital signalprocessor (DSP) 132 can include a high-rate hardware-based DSP 210 and alower-rate software-based DSP 220. High-rate DSP 210 can be a suitabletype of programmable logic device or application-specific integratedcircuit performing high-rate digital signal processing for basebandtranslation of receiver 100. For example, high-rate DSP 210 canimplement signal processing blocks 38, 40, 64, and 66 of receiver 10 ofthe '341 patent, as illustrated in FIG. 8 of that patent. Low-rate DSP220 can be a suitable type of software-programmable DSP (e.g., of thetype available from Analog Devices, Texas Instruments, etc.) forperforming low-rate digital signal processing after decimation byhigh-rate DSP 210. For example, low-rate DSP 220 can implement signalprocessing blocks 70, 68, 72, 74, and 76 of receiver 10 of the '341patent.

During vector mismatch calibration according to various aspects of thepresent invention, low-rate DSP 220 acquires observed samples from the Iand Q inputs of DSP 132. Although the samples at these inputs areprovided at a high sample rate (at the non-decimated input of high-rateDSP 210), only a relatively limited number of samples needs to beprocessed at a time during vector mismatch calibration. Consequently,low-rate DSP 220 can acquire a block of samples, perform vector mismatchcalibration on that block (e.g., using one of exemplary methods 500,600,and 700), store the results of that particular calibration, and repeatthe process on another block of samples when available processing timeof DSP 220 permits. Repeated results of this block processing can bestatistically combined (e.g., averaged) to more accurately determineand/or correct vector mismatch.

Baseband translation performed by DSP 220 can be interrupted for vectormismatch calibration, or the two functions can be performedconcurrently. In receiver 100 of FIG. 1, for example, translation of anRF signal of interest to baseband can be interrupted (stoppedmomentarily), preferably for a short enough time to be unobtrusive to auser or between packets of data transmission. When receiver 100 isinterrupted for vector mismatch calibration, switch 106 can couplemixers 112 and 114 to calibration signal subsystem 150 instead offront-end stage 104. Switch 106 is conceptually a single pole-double,throw-switch, preferably implemented as a solid-statealternating-conduction device such as a suitable type of PIN diode. In avariation, a weakly coupled link can be employed to couple calibrationsignal subsystem 150 to mixers 112 and 114.

Three methods of sample modeling and mismatch determination according tovarious aspects of the present invention to derive an unknown parametervector {circumflex over (β)} may be better understood with reference toflow diagrams of FIGS. 5-7 and appendices A, B, and C of the '226application. The various aspects of the invention disclosed herein andset forth particularly by the exemplary claims below are not limited inany way to the disclosure set forth in the appendices. Further, somestatements made in the appendices only apply within a relatively narrowcontext of communications systems toward which a particular appendix isdirected. Descriptions of the appendices are provided in TABLE II below.TABLE II Appendix Description of Relevance to the Application A From “AnOptimized Multi-Tone Calibration Signal for Quadrature ReceiverCommunication Systems,” submitted by R. A. Green for publication to the10th IEEE Workshop on Statistical Signal and Array Processing and nowpublished as: IEEE Workshop on Statistical Signal and Array Processing,Aug. 14-16, 2000, pp. 664-667. (Incorporated herein by reference.) Thisappendix discloses a phase-optimized multi-tone calibration signalaccording to various aspects of the present invention. A three-toneversion of this particularly advantageous type of calibration signal isemployed in the simulation of FIGS. 8-12. B From “A SDB-SC Signal Modelfor Nonlinear Regression-Based Quadrature Receiver Calibration,” listingR. A. Green as author, Proceedings ICASSP 1999, Phoenix, AZ, Mar. 15,1999, incorporated herein by reference. This appendix presents atwo-tone calibration signal consistent with the nonlinear regressiontechniques presented in Appendix A. This appendix illustrates some ofthe difficulties involved in construction of alternate calibrationsignals such as multitone calibration signals. In particular, theappendix details an undesired phase parameter PSI that results frommodulating a baseband calibration signal with a carrier tone, andprovides a method to accommodate the undesired phase parameter. Phaseadjuster 156 of receiver 100 addresses undesired phase offset introducedby modulating a calibration signal with a carrier signal. C From“Quadrature Receiver Mismatch Calibration,” listing R. A. Green, R. C.Anderson-Sprecher, and J. W. Pierre as coauthors, IEEE Transactions onSignal Processing; Vol 47, No. 11, November 1999, incorporated herein byreference. This appendix introduces quadrature receiver calibration overmultiple frequencies using nonlinear regression techniques. In thisreference, mismatch at each frequency is estimated separately throughrepeated application of a single-tone calibration signal. Some aspectsof the present invention are according to this disclosure, but otheraspects offer particular advantages including: simultaneous calibrationover multiple frequencies using multitone calibration signals; linearregression models that admit closed-form, real time estimation; andgeneralization to multiple signal path systems such as array processors.D Matlab (RTM The Mathworks, Inc.) source code for the simulations ofFIGS. 8-25. This code provides a conceptual-level context for thesimulation plots. However, it does not carry out an exhaustivesimulation of an actual communications system during operation ofvarious aspects of the invention.

Subsystem 410 of exemplary vector calibration system 400 collectsobservation values and generates an estimate of the unknown parametervector, {circumflex over (β)}. For quadrature receiver 100 of FIG. 1,observations are taken from the in-phase and quadrature branches, assampled and digitized by A/D converters 120 and 122. In variations suchas multi-sensor array processors, observations can be taken from othertypes of signal paths. Typically data are collected simultaneously fromeach signal path at a uniform sampling rate. However, a calibrationsystem according to various aspects of the present invention permitsnon-uniform sampling as well as sampling of signal paths at differenttimes.

Subsystem 410 normally employs one of two general class of algorithm.Recursive algorithms provide new parameter estimates with each newobservation set. Non-recursive algorithms provide parameter estimatesless frequently; typically estimates are computed after a block ofsamples is collected. Deterministic least squares, for example, istypically a non-recursive algorithm that post-processes data. Adaptivetechniques are often recursive and permit real-time parameterestimation. Real-time operation is important to accommodate systems thatpossess slow time variations in the unknown parameters β.

Many methods exist to estimate the unknown parameters. When observationsare expressed as a linear combination of basis functions and unknownparameters plus noise (Y=Xβ+ε), efficient parameter estimation isaccomplished using techniques such as deterministic least-squares oradaptive techniques such as the Least Mean Square (LMS) algorithm andthe Exponential Forgetting Window Recursive Least Squares (EFW-RLS)algorithms. Guidance as to implementation of such techniques may befound in Simon Haykin, “Adaptive Filter Theory”, 2nd edition, PrenticeHall Inc., 1991, referred to herein as “Haykin” and incorporated hereinby reference. FIGS. 5, 6, and 7 illustrate methods 500, 600, and 700 ofrecursive parameter estimation (given a linear model) usingdeterministic least-squares, LMS, and EFW-RLS, respectively. Sometimesthe calibration signal requires a nonlinear model. In these cases,nonlinear regression techniques can be applied to generate parameterestimates, as discussed in Appendix A.

Algorithm 500 illustrates a recursive implementation of deterministicleast squares. This approach is taken for consistency with methods 600and 700. However, the computational burden of this implementation ofdeterministic least squares increases with the amount of data collected,so it is not often used in practice. Rather, deterministic least squaresnormally post-processes data to estimate unknown parameters. In avariation of method 500 for standard post-processing, step 540 isskipped until all data is collected.

Method 500 begins at step 505. Step 510 is executed once to initializesystem parameters. Specifically, a sample index n is set to zero, anobservation vector Y_(n) is cleared, and a basis function matrix X_(n)is also cleared. The types of elements of X_(n) depend on the particularcalibration signal employed, as well as the number of frequencies atwhich vector mismatch is to be determined.

Step 515 begins the main loop of the algorithm by incrementing thesample index n. Step 520 acquires and stores samples of the observationy[n]. Method 500 can be applied to signal paths separately or incombinations, e.g., with I and Q samples interleaved. If method 500 isapplied to each signal path separately, y[n] is simply a sample of thatsignal path at time index n. If method 500 is applied to the collectionof signal paths, samples from each signal path are typically stackedinto y[n]. Deterministic least squares requires all data points to besaved, so the new sample is stored into a vector of observations Y_(n)that contains all samples from beginning step 515 to the current timeindex n.

Step 525 computes the known basis functions X[n] for the current indexn. Computation can be avoided through the use of a data look up table.The length of this row vector depends on the number of signal pathsbeing processed, the calibration signal, and the number of frequencybins of interest. For example, calibration of mismatch betweenquadrature signal paths using a calibration signal with three tonesrequires that X[n] is a length-6 row vector. In this example,X[n]=[cos({tilde over (w)}₁t+θ₁),sin({tilde over (w)}₁t+θ₁),cos({tildeover (w)}₂t+θ₂),sin({tilde over (w)}₂t+θ₂),cos({tilde over(w)}₃t+θ₃),sin({tilde over (w)}₃t+θ₃)] where {tilde over (w)} are thecalibration tone frequencies and θ are the optimized phases.Simultaneous processing of both the I and Q branches using the samecalibration signal requires that X[n] is a length-12 vector. The rowvector X[n] is stored into the n^(th) row of the matrix X_(n).

Step 540 determines the parameter estimate using the equation{circumflex over (β)}_(n)=(X_(n) ^(H)X_(n))⁽⁻¹⁾X_(n) ^(H)Y_(n). Here,⁽⁻¹⁾ designates a matrix inverse operation and ^(H) indicates thecomplex-conjugate transpose operation. As indicated above, standarddeterministic least-squares would skip step 540 until all data had beencollected. By applying method 500 to relatively short-length data sets,however, non-stationarities in the parameters β can be accommodated. Thecolumn vector β has the same length as X[n].

An exemplary implementation of vector calibration with the LMS algorithmmay be better understood with reference to FIG. 6. The computationalburden of the LMS algorithm remains constant with the addition of data.The LMS algorithm is very simple to implement, and thus it is relativelyeasy to achieve real-time operation even with relatively modest DSPresources. LMS does not converge as quickly as other adaptivealgorithms, but the robust nature of the algorithm has made it a popularchoice in adaptive signal processing applications.

A bounded version of the LMS algorithm has been shown to have desirableconvergence behavior. The bounded version simply constrains the valuesattained by the algorithm to a pre-determined bounded region. Furtherinformation instructive for implementing the bounded version of the LMSalgorithm is found in D. C. Farden, “Tracking Properties of AdaptiveSignal Processing Algorithms,” IEEE Trans. Acoust., Speech, and SignalProcessing, ASSP-29, June 1981, pp. 439-446, incorporated herein byreference. In a bounded version of method 600, step 640 is suitablymodified.

Method 600 of FIG. 6 begins at step 605. Step 610 is executed once toinitialize system parameters. Specifically, the sample index n is set tozero, the initial parameter estimates {circumflex over (β)}₀ are set tonominal values, and the step-parameter μ is set according to particularconditions of the communications system in which method 600 isimplemented, e.g., receiver 100. The step parameter μ affectsconvergence rates as well as the ability of the algorithm to tracktemporal variations in the unknown parameters β. Published referencessuch as Haykin provide basic rules for establishing μ. As a generalrule, μ is a small value. For systems with little or no parametervariation, small μ can reduce estimate variance but also slowsconvergence. Larger μ allows the algorithm to track more rapid parametervariations but with less accuracy.

Step 615 begins the main loop of method 600 by incrementing the sampleindex n. Step 620 acquires and stores the observation y[n]. Method 600can be applied to signal path separately or in combination. If method600 is applied to each signal path separately, y[n] is simply a sampleof that signal path at time index n. If method 600 is applied tomultiple signal paths, samples from each signal path can be interleavedinto y[n]. Only the current set of observations needs to be stored inmethod 600.

Step 625 computes the known basis functions X[n] for the current indexn. Computation can be avoided through the use of a data look-up table.The length of this column vector depends on the number of signal pathsbeing processed as well as the number of frequency bins of interest. Forexample, quadrature mismatch calibration of a quadrature receiver usinga calibration signal with three tones requires that X[n] is a length-6column vector. In this example, ${X\lbrack n\rbrack} = \begin{bmatrix}{\cos\left( {{\varpi_{1}t} + \theta_{1}} \right)} \\{\sin\left( {{\varpi_{1}t} + \theta_{1}} \right)} \\{\cos\left( {{\varpi_{2}t} + \theta_{2}} \right)} \\{\sin\left( {{\varpi_{2}t} + \theta_{2}} \right)} \\{\cos\left( {{\varpi_{3}t} + \theta_{3}} \right)} \\{\sin\left( {{\varpi_{3}t} + \theta_{3}} \right)}\end{bmatrix}$where {tilde over (Ω)} are the calibration tone frequencies and θ areoptimized phases, selected to minimize the peak amplitude of the signal.Simultaneous processing of two signal paths (e.g., I and Q) using thesame calibration signal requires X[n] to be a length-12 vector. Only thebasis functions for the current index are required.

In a variation, basis functions can be complex exponentials instead ofsines and cosines. Conceptually, the two types of basis functions arethe same. However, with complex exponentials, a single basis functionsforms orthogonal basis for a single tone. With sines and cosines, twobasis functions for an orthogonal basis for a single tone.

Step 630 computes a gain term k[n]=μ[n]. The gain term is used to weightthe error term e[n]=y[n]−β_(n−1) ^(H)X[n] computed in step 635. Theunknown parameter vector is estimated in step 630 according to {tildeover (β)}_(n)={tilde over (β)}_(n−1)+k[n]e*[n]. Here, * representscomplex conjugation. The column vector β has the same dimension as X[n].

An exemplary implementation of vector calibration with an “exponentialforgetting window-recursive least squares” algorithm according tovarious aspects of the present invention may be better understood withreference to FIG. 7. The computational burden of the LMS algorithmremains constant with the addition of data. EFW-RLS converges morequickly than LMS, but performance is not as robust to model deviations.The EFW-RLS algorithm is moderately complex to implement, but real-timeoperation is still possible using today's modern DSP technology.

Method 700 of FIG. 7 begins at step 705. Step 710 is executed once toinitialize system parameters. Specifically, a sample index n is set tozero, an initial parameter estimates {tilde over (β)}₀ are set tonominal values, and a “forgetting factor” λ is set according toparticular communication system conditions. The forgetting factoraffects convergence rates as well as the ability of the algorithm totrack temporal variations in the unknown parameters β. Publishedreferences such as Haykin provide basic rules for establishing λ. Bysetting the forgetting factor to one, there is no loss and the resultsare similar to deterministic least squares. For λ<1, old data are givenless weight. This approach allows temporal variation of parameters, asis typical with component drift in analog systems. A parameter P used incomputations is initialized to P[0]=δ⁻¹I. Here, δ is a small positiveconstant (Haykin provides pertinent details) and I is an identity matrixwith dimension equal to the number of unknown parameters. (The matrix“I” of this example is not to be confused with the in-phase signal pathlabeled “I” in FIG. 4.)

Step 715 begins the main loop of method 700 by incrementing the sampleindex n. Step 720 acquires and stores the observation y[n]. Method 700can be applied to signal path, separately or in combination. If method700 is applied to each signal path separately, y[n] is simply a sampleof that signal path at time index n. If method 700 is applied tomultiple signal paths, samples from each signal path can be interleavedinto y[n]. Only the current set of observations needs to be stored inmethod 700.

Step 725 computes the known basis functions X[n] for the current indexn. Computation can be avoided through the use of a data look up table.The length of this column vector depends on the number of signal pathsbeing processed as well as the number of frequency bins of interest. Forexample, I-branch processing of a quadrature receiver using acalibration signal with three tones requires that X[n] is a length-6column vector. In this example, ${X\lbrack n\rbrack} = \begin{bmatrix}{\cos\left( {{\varpi_{1}t} + \theta_{1}} \right)} \\{\sin\left( {{\varpi_{1}t} + \theta_{1}} \right)} \\{\cos\left( {{\varpi_{2}t} + \theta_{2}} \right)} \\{\sin\left( {{\varpi_{2}t} + \theta_{2}} \right)} \\{\cos\left( {{\varpi_{3}t} + \theta_{3}} \right)} \\{\sin\left( {{\varpi_{3}t} + \theta_{3}} \right)}\end{bmatrix}$where {tilde over (w)} are the calibration tone frequencies and θ areoptimized phases. Simultaneous processing of both the I and Q branchesusing the same calibration signal requires that X[n] is a length-12vector. Only the basis functions for the current index are required.

Step 730 computes a gain termk[n]=λ⁻¹P[n−1]X[n]/{1−λ⁻¹X^(H)[n]P[n−1]X[n]}. In this expression, P is avariable defined simply for convenient computation. The gain term isused to weight the error term e[n]=y[n]−{tilde over (β)}_(n−1) ^(H)X[n]computed in step 635. The unknown parameter vector is estimated in step730 according to {tilde over (β)}_(n)={tilde over (β)}_(n−1)+k[n]e* [n].Here, * represents complex conjugation. Finally, step 745 computes thenext value of P, P[n]=λ⁻¹P[n−1]−λ⁻¹k[n]X^(H)[n]P[n−1], which is neededfor the next recursion.

While the present invention has been described in terms of preferredembodiments and generally associated methods, the inventors contemplatethat alterations and permutations of the preferred embodiments andmethod will become apparent to those skilled in the art upon a readingof the specification and a study of the drawings. For example, vectormismatch between signal paths of an array processor can be determinedinstead of mismatch between quadrature signal paths of a quadraturereceiver.

An exemplary array processor 2600 employing vector mismatch calibrationaccording to various aspects of the present invention may be betterunderstood with reference to FIG. 26. Array processor 2600 includesconventional circuitry for superheterodyne RF frequency translation anddigital array processor of translated signals. The circuitry includesfront-end stages 2622 and 2624 coupled to image-reject filters 2632 and2634, which are in turn coupled to mixers 2642 and 2644, which arecoupled to IF stages 2652 and 2654. Digital subsystem 2660 digitizessignal that are suitably selected and amplified by IF stages 2652 and2654 and performs array processing on the digitized signals. Mixers 2642and 2644 are fed by local oscillator signals from local oscillator 2670.

Array processor 2600 further includes circuitry for implementing vectormismatch calibration according various aspects of the present invention.The circuitry includes calibration signal subsystem 2680, amplifier2685, RF transmission path 2687, another amplifier 2610, an antenna2612. Calibration signal subsystem 2680 generates a phase-coherentcalibration signal (as is preferred) and sends the signal to amplifier2685, which amplifies the signal for transmission through transmissionpath 2687. Amplifier 2610 further amplifies the signal for transmissionthrough antenna 2612. Antenna 2612 is suitably placed at a predetermined(or fixed) position with respect to array elements coupled to amplifiers2622 and 2624. Because the position of 2612 with respect to the arrayelements is fixed, desired or known calibration signals can be modeledagainst signals received from IF stages 2652 and 2654. Thus, vectormismatch can be determined and/or corrected between a signal path forone array element (e.g., including front-end stage 2622, image-rejectfilter 2632, mixer 2642, and IF stage 2652) and a signal path foranother array element (e.g., including front-end stage 2624,image-image-reject filter 2634, mixer 2644, and IF stage 2654).

Although a predetermined position for antenna 2612 is preferred, antenna2612 can be placed at an unknown but fixed far-field location in anadvantageous variation of array processor 2600. In such a variation, apredetermined phase relationship still exists among the array elementscoupled to amplifiers 2622 and 2624, but the relationship is dependenton an unknown angle of arrival. Array processor 2600 can estimate thisangle of arrival using conventional techniques (e.g., beamforming, MVDR,MUSIC, root-MUSIC, etc.) and then correct any mismatch. In a furthervariation, array processor 2600 can update adaptive filtering algorithmsto correct mismatch without needing to provide an estimate of the angleof arrival.

Accordingly, neither the above description of preferred exemplaryembodiments nor the abstract defines or constrains the presentinvention. Rather, the issued claims variously define the presentinvention. Each variation of the present invention is limited only bythe recited limitations of its respective claim, and equivalentsthereof, without limitation by other terms not present in the claim.Further, aspects of the present invention are particularly pointed outbelow using terminology that the inventors regard as having its broadestreasonable interpretation; the more specific interpretations of 35U.S.C. §112(6) are only intended in those instances where the term“means” is actually recited.

In addition, the inventors contemplate that their inventions include allmethods that can be practiced from all suitable combinations of themethod claims filed with the application, as well as all apparatus andsystems that can be formed from all suitable combinations of theapparatus and system claims filed with the application.

1. A method for calibrating a signal processing system to minimizevector mismatch between signals frequency translated from an RF signaland conveyed along a plurality of signal paths of the signal processingsystem, the method comprising: (a) applying a calibration signal havinga plurality of tones to the signal processing system, such that thecalibration signal is frequency translated; (b) sampling thefrequency-translated calibration signal (1) along a first signal path ofthe signal processing system to obtain a first set of observed samplesand (2) along a second signal path of the signal processing system toobtain a second set of observed samples; (c) filtering the first set ofobserved samples with an adaptive filter having adaptable coefficientsto obtain a set of filtered samples; and (d) adapting the coefficientsto minimize undesired deviations between the set of filtered samples andthe second set of observed samples.
 2. The method of claim 1 furthercomprising using the filter with the adapted coefficients to minimizevector mismatch between signals frequency-translated by the signalprocessing system from an RF input signal of interest and conveyed alongthe first and second signal paths.
 3. The method of claim 1 furthercomprising generating the calibration signal.
 4. The method of claim 3wherein generating the calibration signal comprises: (a) generating alocal oscillator signal, which signal the signal processing system usesto perform frequency translation; (b) generating a baseband calibrationsignal; and (c) mixing the local oscillator signal with the basebandcalibration signal, thereby obtaining a radio frequency calibrationsignal.
 5. The method of claim 1 wherein: (a) the signal paths includean in-phase signal path and a quadrature signal path; and (b) the filtercoefficients are adapted to minimize deviations from a quadraturerelationship between a signal on the in-phase signal path and a signalon the quadrature signal path.
 6. The method of claim 1 wherein: (a) thesignal paths include a plurality of signal paths coupled to respectiveelements of a spatially selective array; and (b) the filter coefficientsare adapted to minimize deviations from a predetermined phase andamplitude relationship between signals on each respective one of theplurality of signal paths, such deviations degrading spatial selectivityof the array.
 7. The method of claim 6 further comprising generating thecalibration signal and transmitting it through an antenna placed at afixed position with respect to the array elements.
 8. The method ofclaim 1 wherein adapting is performed by a least mean squares algorithm.9. The method of claim 8 wherein a plurality of values are determined byleast mean squares constrained to a predetermined bounded region. 10.The method of claim 1 wherein: (a) the signal paths include an in-phasesignal path and a quadrature signal path; and (b) the filtercoefficients are adapted by a least mean squares algorithm to minimizedeviations from a quadrature relationship between a signal on thein-phase signal path and a signal on the quadrature signal path.
 11. Themethod of claim 10 further comprising: (a) generating the calibrationsignal; and (b) after adapting the filter coefficients, using the filterwith the adapted coefficients to minimize deviations in a quadraturerelationship between in-phase and quadrature signalsfrequency-translated by the signal processing system from an RF inputsignal of interest.
 12. A signal processing system comprising: (a) afrequency translation subsystem structured to produce a plurality offrequency-translated signals responsive to a calibration signal having aplurality of tones; (b) one or more converters coupled to the frequencytranslation subsystem and structured to convert the signals into aplurality of sets of observed samples; (c) an adaptive filter havingadaptable coefficients and structured to produce a set of filteredsamples responsive to one of the sets of observed samples; and (d)control circuitry structured to adapt the filter coefficients tominimize undesired deviations between the set of filtered samples and adifferent one of the sets of observed samples.
 13. The system of claim12 further comprising a calibration signal subsystem coupled to thefrequency translation subsystem and structured to produce thecalibration signal.
 14. The system of claim 12 wherein: (a) theplurality of frequency-translated signals consists of an in-phase signaland a quadrature signal; (b) the plurality of sets of observed samplesconsists of two sets of observed samples, one converted from thein-phase signal and the other converted from the quadrature signal; and(c) the undesired deviations are deviations from a quadraturerelationship between the in-phase signal and the quadrature signal. 15.The system of claim 12 wherein: (a) the frequency-translated signals arefrom respective elements of a spatially selective array; and (b) theundesired deviations are deviations from a predetermined phase andamplitude relationship between signals on each respective one of theplurality of signal paths, such deviations degrading spatial selectivityof the array.
 16. The system of claim 12 further comprising: (a) afront-end stage structured to produce a selectively amplified RF signalresponsive to RF input; (b) wherein the frequency translation subsystemis further coupled to the front-end stage and structured to producefrequency-translated in-phase and quadrature signals responsive to theselectively amplified RF signal from the front-end stage.
 17. The systemof claim 16 further comprising a switch coupled to the calibrationsignal subsystem and the front-end stage, and structured to convey aselected one of the calibration signal and the selectively amplified RFsignal to the frequency translation subsystem for frequency translationinto the in-phase and quadrature signals.
 18. The system of claim 12wherein the control circuitry is structured to adapt the filtercoefficients by a least mean squares algorithm that determines aplurality of values by least mean squares constrained to a predeterminedbounded region.
 19. The system of claim 12 further comprising: (a) aswitch; (b) a calibration signal subsystem selectably coupled to thefrequency translation subsystem via the switch and structured to producethe calibration signal; and (c) a front-end stage selectably coupled tothe frequency translation subsystem via the switch and structured toproduce a selectively amplified RF signal responsive to RF input; (d)wherein the frequency translation subsystem is structured to producefrequency-translated in-phase and quadrature signals responsive toeither one of (1) the calibration signal, and (2) the selectivelyamplified RF signal from the front-end stage.
 20. The system of claim 19wherein: (a) the plurality of frequency-translated signals consists ofan in-phase signal and a quadrature signal; (b) the plurality of sets ofobserved samples consists of two sets of observed samples, one convertedfrom the in-phase signal and the other converted from the quadraturesignal; and (c) the undesired deviations are deviations from aquadrature relationship between the in-phase signal and the quadraturesignal.
 21. The system of claim 20 wherein the control circuitry isstructured to adapt the filter coefficients by a least mean squaresalgorithm that determines a plurality of values by least mean squaresconstrained to a predetermined bounded region.
 22. A signal processingsystem comprising: (a) means for generating a calibration signal havinga plurality of tones; (b) means for producing a plurality offrequency-translated signals responsive to the calibration signal; (c)means for producing filtered samples from one of thefrequency-translated signals, using a set of adaptable coefficients; and(d) means for adapting the filter coefficients to minimize undesireddeviations between the filtered samples and a different one of thefrequency-translated signals.
 23. The system of claim 22 furthercomprising means for receiving and frequency translating an RF inputsignal to the plurality of frequency-translated signals with undesireddeviations between the signals minimized by the adaptation of the filtercoefficients.
 24. The system of claim 22 wherein the plurality offrequency-translated signals consists of an in-phase signal and aquadrature signal and the undesired deviations are deviations from aquadrature relationship between the two signals.
 25. The system of claim22 wherein the calibration signal is phase-synchronous with a localoscillator signal employed for producing a plurality offrequency-translated signals responsive to the calibration signal.